Design a data structure that supports insertion, deletion, and random element retrieval, all in constant time on average. You'll need to handle edge cases carefully to achieve O(1) complexity.

Given a grid representing land and water, count the number of distinct islands. An island is formed by connected land cells.

Design a data structure that efficiently stores a set of strings and allows for prefix-based searches. Implement methods to insert strings, search for complete words, and check if any word starts with a given prefix.